Problem: Evaluate the definite integral. $\int^1_{2}-4x^{-3}\,dx = $
First, use the power rule: $\int^1_{2}-4x^{-3}\,dx ~=~2x^{-2}\Bigg|^{1}_{{2}}$ Second, plug in the limits of integration: $[2\cdot1^{-2}]-[2\cdot2^{-2}] = 2-0.5 = 1.5$. The answer: $\int^1_{2}-4x^{-3}\,dx = 1.5$